public ShapeMatching(GameObject points)
{
//Instantiation method for shapematching object
//Stores duplicates of points passed in to object as an array of original positions to be used in calculation
particles = points;
Transform [] original_transforms = particles.GetComponentsInChildren <Transform>();
original_positions = new Vector3[original_transforms.Length - 1];
for (int i = 1; i < original_transforms.Length; i++) //i starts at one in order to avoid origin being added to positions
{
original_positions[i - 1] = particles.transform.InverseTransformPoint(original_transforms[i].position);
cm0 += original_positions[i - 1];
}
cm0 /= original_positions.Length;
//Precalculates Aqq from original positions
aqq = new double [, ] {
{ 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }
};
for (int i = 0; i < original_positions.Length; i++)
{
original_positions[i] -= cm0;
MatrixFunctions.matrix_add_3x3(ref aqq, MatrixFunctions.vector3_covariance(original_positions[i], original_positions[i]));
}
//performs inverse operation on Aqq matrix as stated in Muller paper
MatrixFunctions.matrixInverse3x3(ref aqq);
}
public double [,] generate_linear_matrix(Vector3 [] new_positions, double beta)
{
double [,] r = generate_rotation_matrix(new_positions);
double [,] a = MatrixFunctions.matrixMultiply3x3(apq, aqq);
//Rotation_test.print_matrix(aqq);
double determinant = alglib.rmatrixdet(a);
determinant = Mathf.Pow((float)determinant, 1.0f / 3.0f);
MatrixFunctions.scalar_multiply(ref a, beta / determinant);
MatrixFunctions.scalar_multiply(ref r, 1 - beta);
MatrixFunctions.matrix_add_3x3(ref a, r);
return(a);
}
public double [,] generate_rotation_matrix(Vector3 [] new_positions)
{
//3x3 matrix of zeros used for summation
apq = new double [, ] {
{ 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }
};
for (int i = 0; i < original_positions.Length; i++)
{
MatrixFunctions.matrix_add_3x3(ref apq, MatrixFunctions.vector3_covariance(new_positions[i], original_positions[i]));
//CHECKED: new positions are different from old ones, seem consitent
}
//CHECKED THROUGH THIS POINT
s = MatrixFunctions.matrixMultiply3x3(MatrixFunctions.transpose3x3(apq), apq);
MatrixFunctions.matrixInverseSquareRoot(ref s);
double [,] r = MatrixFunctions.matrixMultiply3x3(apq, s);
return(r);
}